perplexus.info :: Just Math : Q and A

Q and A (Posted on 2022-03-06)

Q(posed by a high-school student to his math teacher):
Could you tell my age after I disclose the fact that the current number of years of my existence equals the sum of digits representing my age plus their product?
A(provided after 2 minutes of pondering upon the subject): Yes, I have figured out your age, but I must tell you that if the question was posed by phone by a stranger whom I do not see I would not be able to solve this problem.

Please comment about this dialog.

See The Solution Submitted by Ady TZIDON

Rating: 5.0000 (1 votes)

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Solution

| Comment 1 of 2

Let the student's age be a 2 digit number xy (concatenated). For now, allow zero as a possible value for x to account for single digit ages.

The student's statement is represented by:

(10x + y) = x + y + x*y

9x = x*y

9 = y (oops, did I just divide by zero?)

So far, the age can be any 2 digit number ending in 9. Even 09 satisfies this mathematically. But if the student's age is the single digit 9, then the statement becomes:

9 = 9 + 9 which fails. (I guess I shouldn't have divided by zero)

So the possible ages are {19, 29, 39, etc}

Since it is given that the student is in high school,

the only possible answer is 19.

Edited on March 6, 2022, 7:16 am

Posted by Larry on 2022-03-06 07:13:40

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